Sina+sin^2a=1,cos^2a+cos^s4a+cos^6a
问题描述：
Sina+sin^2a=1,cos^2a+cos^s4a+cos^6a
答
设sina=t
t+t^2=1
t^2+t-1=0
delta=1+4=5
t1=-1+√5/2
t2=-1-√5/2(舍)
sina=√5-1/2
cos^2A+cos^6A
=sinA+sin^3A
=sinA+sinA(1-sinA)
=sinA+sinA-(sinA)^2
=2sinA-sin^2A
=2sinA-(1-sinA)
=3sinA-1
=3*√5-1/2-1
=3√5-5/2
答
化简有sinθ=cos^2θ
同时乘以sinθ
sin^2θ+sin^3θ=sinθ
∴sin^3θ=sinθ-sin^2θ=cos^2θ-sin^2θ=cos2θ
∴=sinθ+sin^2θ+sin^3θ
=1+sin^3θ
=1+cos2θ
=2cos^2θ
=2sinθ
又sin²θ+sinθ-1=0 解出